Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases calculated from the sum of the user group releases. The proportion of total rockfish harvested by user group, \(pH_{ayu}\), was assumed to be the mean of \(pH_{(pelagic)ayu}\), \(pH_{(yelloweye)ayu}\) and \(pH_{(nonpel-nonYE)ayu}\) weighted by the relative harvest \(H_{(comp)ayu}\) such that

\[\begin{equation} R_{ayu}~=~ \frac{\sum ({H_{(comp)ayu} * pH_{(comp)ayu})}}{\sum {H_{(comp)ayu}}} \end{equation}\]

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

**Figure 13.**- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
mu_bc_H 1 2.775606
beta3_pH 20 2.628639
beta1_pH 11 2.430289
sd_bc_H 1 2.114784
beta1_pelagic 4 2.046966
beta2_pH 23 1.925556
beta0_pelagic 4 1.847309
beta3_pelagic 2 1.655811
tau_beta0_pH 8 1.618777
beta0_pH 27 1.617359
parameter n badRhat_avg
tau_beta0_pelagic 2 1.383297
mu_beta0_pH 2 1.328844
beta1_yellow 3 1.323355
beta3_yellow 3 1.311134
beta_H 6 1.307020
beta2_pelagic 3 1.297761
beta0_yellow 3 1.287964
beta2_yellow 4 1.230216
beta4_pelagic 1 1.210515
tau_beta0_yellow 1 1.113771
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
beta0_pelagic 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0
beta0_pH 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
beta0_yellow 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0
beta1_pelagic 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0
beta1_pH 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1
beta1_yellow 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0
beta2_pelagic 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0
beta2_pH 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1
beta2_yellow 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0
beta3_pelagic 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1
beta3_yellow 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0
beta4_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
mu_bc_H 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
mu_beta0_pH 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
sd_bc_H 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
tau_beta0_pelagic 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.128 0.078 -0.267 -0.134 0.041
mu_bc_H[2] -0.102 0.042 -0.175 -0.104 -0.011
mu_bc_H[3] -0.430 0.073 -0.568 -0.431 -0.280
mu_bc_H[4] -0.983 0.188 -1.359 -0.978 -0.620
mu_bc_H[5] 0.778 0.786 -0.208 0.614 2.692
mu_bc_H[6] -2.199 0.340 -2.856 -2.209 -1.492
mu_bc_H[7] -0.480 0.117 -0.721 -0.475 -0.261
mu_bc_H[8] 0.278 0.386 -0.341 0.237 1.203
mu_bc_H[9] -0.297 0.130 -0.537 -0.300 -0.035
mu_bc_H[10] -0.123 0.071 -0.257 -0.125 0.017
mu_bc_H[11] -0.105 0.039 -0.178 -0.106 -0.022
mu_bc_H[12] -0.250 0.106 -0.473 -0.247 -0.051
mu_bc_H[13] -0.119 0.079 -0.270 -0.119 0.035
mu_bc_H[14] -0.293 0.094 -0.483 -0.291 -0.113
mu_bc_H[15] -0.285 0.099 -0.436 -0.308 -0.080
mu_bc_H[16] -0.191 0.387 -0.858 -0.224 0.726
mu_bc_R[1] 1.465 0.172 1.137 1.463 1.807
mu_bc_R[2] 1.509 0.077 1.346 1.512 1.656
mu_bc_R[3] 1.396 0.149 1.106 1.400 1.678
mu_bc_R[4] 0.994 0.218 0.524 1.010 1.390
mu_bc_R[5] 1.215 0.450 0.316 1.227 2.072
mu_bc_R[6] -1.544 0.437 -2.384 -1.544 -0.653
mu_bc_R[7] 0.508 0.228 0.057 0.516 0.923
mu_bc_R[8] 0.535 0.192 0.152 0.542 0.911
mu_bc_R[9] 0.440 0.187 0.031 0.456 0.770
mu_bc_R[10] 1.375 0.158 1.064 1.375 1.690
mu_bc_R[11] 1.190 0.057 1.080 1.191 1.302
mu_bc_R[12] 1.036 0.149 0.722 1.043 1.328
mu_bc_R[13] 1.057 0.098 0.864 1.058 1.242
mu_bc_R[14] 1.048 0.130 0.781 1.054 1.288
mu_bc_R[15] 0.853 0.116 0.644 0.845 1.099
mu_bc_R[16] 1.162 0.107 0.938 1.167 1.365
tau_pH[1] 3.115 0.296 2.577 3.109 3.712
tau_pH[2] 0.765 0.408 0.400 0.517 1.557
tau_pH[3] 2.789 0.422 2.045 2.763 3.699
tau_pH[4] 9.094 3.286 4.560 8.501 16.994
tau_pH[5] 4.787 1.628 2.292 4.565 8.618
beta0_pH[1,1] 0.690 0.210 0.268 0.694 1.085
beta0_pH[2,1] 1.177 0.251 0.595 1.186 1.642
beta0_pH[3,1] 1.239 0.324 0.560 1.260 1.801
beta0_pH[4,1] 1.443 0.353 0.753 1.454 2.092
beta0_pH[5,1] -1.232 0.361 -1.977 -1.225 -0.576
beta0_pH[6,1] -0.914 0.596 -2.279 -0.837 0.041
beta0_pH[7,1] 0.385 0.371 -0.509 0.501 0.853
beta0_pH[8,1] -0.876 0.344 -1.710 -0.835 -0.296
beta0_pH[9,1] -1.000 0.506 -2.184 -0.931 -0.186
beta0_pH[10,1] 0.547 0.203 0.132 0.546 0.931
beta0_pH[11,1] 0.491 0.829 -1.118 0.760 1.653
beta0_pH[12,1] 0.620 0.216 0.181 0.621 1.030
beta0_pH[13,1] -0.433 0.278 -1.011 -0.422 0.071
beta0_pH[14,1] -0.868 0.351 -1.582 -0.862 -0.203
beta0_pH[15,1] -0.566 0.587 -1.977 -0.514 0.382
beta0_pH[16,1] -0.833 0.993 -2.586 -0.676 0.816
beta0_pH[1,2] 2.613 0.442 1.693 2.644 3.369
beta0_pH[2,2] 2.815 0.361 1.970 2.845 3.443
beta0_pH[3,2] 2.602 0.529 1.579 2.611 3.552
beta0_pH[4,2] 2.684 0.314 1.991 2.705 3.245
beta0_pH[5,2] 3.384 2.159 1.624 3.010 6.848
beta0_pH[6,2] 2.424 1.035 -1.050 2.690 3.510
beta0_pH[7,2] 1.957 0.682 -0.181 2.052 2.795
beta0_pH[8,2] 2.584 0.618 0.818 2.703 3.312
beta0_pH[9,2] 2.865 0.708 1.437 2.894 4.025
beta0_pH[10,2] 3.062 0.801 1.441 3.110 4.241
beta0_pH[11,2] -2.687 0.132 -2.750 -2.735 -2.265
beta0_pH[12,2] -2.707 0.078 -2.750 -2.735 -2.482
beta0_pH[13,2] -2.705 0.086 -2.750 -2.735 -2.474
beta0_pH[14,2] -2.711 0.070 -2.750 -2.736 -2.507
beta0_pH[15,2] -2.699 0.122 -2.750 -2.735 -2.430
beta0_pH[16,2] -2.689 0.136 -2.750 -2.734 -2.264
beta0_pH[1,3] 1.113 0.515 -0.479 1.225 1.682
beta0_pH[2,3] 1.856 0.500 0.630 2.045 2.456
beta0_pH[3,3] 2.032 0.485 0.879 2.095 2.707
beta0_pH[4,3] 2.145 0.770 0.302 2.262 3.116
beta0_pH[5,3] 0.780 1.331 -0.957 0.496 4.551
beta0_pH[6,3] -0.163 0.947 -2.345 0.058 1.123
beta0_pH[7,3] 0.359 0.628 -1.492 0.563 1.013
beta0_pH[8,3] 0.297 0.178 -0.049 0.297 0.635
beta0_pH[9,3] 0.099 0.356 -0.637 0.134 0.711
beta0_pH[10,3] 0.447 0.447 -0.587 0.510 1.137
beta0_pH[11,4] 1.220 0.955 -0.731 1.200 2.812
beta0_pH[12,4] -1.051 1.306 -2.645 -1.554 1.735
beta0_pH[13,4] -0.077 1.569 -2.652 0.619 1.762
beta0_pH[14,4] 1.051 1.086 -1.005 1.049 2.685
beta0_pH[15,4] 1.659 1.144 -0.216 1.541 3.927
beta0_pH[16,4] 1.355 1.029 -1.147 1.672 2.871
beta0_pH[11,5] -0.906 0.218 -1.362 -0.897 -0.496
beta0_pH[12,5] -1.682 0.668 -2.675 -1.733 -0.538
beta0_pH[13,5] -0.530 0.389 -1.354 -0.455 0.075
beta0_pH[14,5] -1.126 0.214 -1.530 -1.128 -0.676
beta0_pH[15,5] -1.144 0.191 -1.516 -1.140 -0.776
beta0_pH[16,5] -0.980 0.384 -1.962 -0.887 -0.453
beta1_pH[1,1] 2.843 0.462 2.094 2.800 3.876
beta1_pH[2,1] 2.436 0.590 1.710 2.338 4.409
beta1_pH[3,1] 2.387 0.612 1.471 2.284 3.764
beta1_pH[4,1] 3.223 0.789 2.012 3.104 5.035
beta1_pH[5,1] 2.574 0.404 1.841 2.553 3.397
beta1_pH[6,1] 3.939 1.046 2.055 3.890 6.169
beta1_pH[7,1] 1.510 1.450 0.123 0.958 5.751
beta1_pH[8,1] 3.945 0.883 2.562 3.792 6.072
beta1_pH[9,1] 2.550 0.582 1.617 2.444 3.897
beta1_pH[10,1] 1.883 0.301 1.349 1.869 2.543
beta1_pH[11,1] 3.033 0.851 1.802 2.772 4.739
beta1_pH[12,1] 2.435 0.269 1.922 2.429 2.969
beta1_pH[13,1] 3.393 0.378 2.689 3.379 4.198
beta1_pH[14,1] 4.170 0.417 3.371 4.164 4.997
beta1_pH[15,1] 3.914 0.662 2.821 3.835 5.405
beta1_pH[16,1] 4.455 1.099 2.666 4.340 6.478
beta1_pH[1,2] 1.704 1.572 0.061 1.273 6.182
beta1_pH[2,2] 1.856 1.718 0.052 1.252 6.151
beta1_pH[3,2] 1.641 1.199 0.140 1.450 5.068
beta1_pH[4,2] 2.745 2.011 0.127 2.393 7.198
beta1_pH[5,2] 3.398 1.977 0.284 3.191 7.959
beta1_pH[6,2] 1.902 1.325 0.142 1.644 5.300
beta1_pH[7,2] 1.773 1.792 0.033 1.142 6.666
beta1_pH[8,2] 1.663 1.592 0.049 1.125 5.916
beta1_pH[9,2] 1.703 1.267 0.133 1.454 5.224
beta1_pH[10,2] 1.901 1.501 0.111 1.530 5.886
beta1_pH[11,2] 3.538 0.872 2.316 3.189 5.062
beta1_pH[12,2] 4.828 0.460 3.952 4.813 5.804
beta1_pH[13,2] 5.206 0.362 4.467 5.211 5.917
beta1_pH[14,2] 4.659 0.399 3.868 4.653 5.472
beta1_pH[15,2] 5.205 0.391 4.400 5.221 5.951
beta1_pH[16,2] 4.354 0.849 3.064 4.069 5.794
beta1_pH[1,3] 2.308 0.739 1.421 2.150 4.470
beta1_pH[2,3] 2.067 1.843 0.126 1.330 6.799
beta1_pH[3,3] 1.244 1.213 0.053 0.927 4.718
beta1_pH[4,3] 1.588 1.342 0.096 1.255 5.405
beta1_pH[5,3] 4.071 1.765 0.930 3.866 8.013
beta1_pH[6,3] 2.869 1.895 0.168 2.553 7.191
beta1_pH[7,3] 1.349 1.364 0.045 0.898 5.481
beta1_pH[8,3] 2.742 0.341 2.082 2.736 3.409
beta1_pH[9,3] 1.969 0.428 1.206 1.946 2.844
beta1_pH[10,3] 2.985 0.534 2.091 2.930 4.189
beta1_pH[11,4] 1.848 1.066 0.125 1.818 4.274
beta1_pH[12,4] 4.133 1.247 1.592 4.570 5.787
beta1_pH[13,4] 3.080 1.790 0.898 2.359 6.583
beta1_pH[14,4] 1.988 1.282 0.151 1.882 5.023
beta1_pH[15,4] 1.976 1.372 0.189 1.702 5.684
beta1_pH[16,4] 1.987 1.182 0.441 1.724 4.686
beta1_pH[11,5] 3.152 1.473 1.343 2.779 6.900
beta1_pH[12,5] 4.765 1.781 1.724 4.594 8.668
beta1_pH[13,5] 3.696 1.214 1.679 3.574 6.481
beta1_pH[14,5] 3.313 1.788 1.007 2.873 7.729
beta1_pH[15,5] 2.661 0.873 1.499 2.510 4.982
beta1_pH[16,5] 2.736 2.024 0.272 2.305 7.362
beta2_pH[1,1] 0.643 0.609 0.241 0.500 2.253
beta2_pH[2,1] 1.015 1.097 0.136 0.657 4.280
beta2_pH[3,1] 1.057 1.201 0.152 0.572 4.449
beta2_pH[4,1] 0.403 0.526 0.128 0.295 1.303
beta2_pH[5,1] 3.387 1.678 1.028 3.072 7.397
beta2_pH[6,1] 0.264 0.469 0.091 0.184 0.817
beta2_pH[7,1] 0.462 3.651 -6.368 0.949 7.034
beta2_pH[8,1] 0.281 0.222 0.128 0.243 0.609
beta2_pH[9,1] 0.780 0.930 0.195 0.517 3.596
beta2_pH[10,1] 1.223 1.114 0.294 0.834 4.577
beta2_pH[11,1] 1.573 1.341 0.477 1.071 5.476
beta2_pH[12,1] 3.198 1.673 1.113 2.802 7.476
beta2_pH[13,1] 0.931 0.620 0.369 0.785 2.363
beta2_pH[14,1] 1.008 0.437 0.555 0.912 2.028
beta2_pH[15,1] 0.737 0.449 0.319 0.628 1.898
beta2_pH[16,1] 0.482 0.498 0.126 0.358 1.509
beta2_pH[1,2] -0.633 3.255 -7.082 -0.516 5.430
beta2_pH[2,2] -1.992 2.709 -7.598 -1.846 3.661
beta2_pH[3,2] -2.471 2.452 -7.737 -2.209 2.370
beta2_pH[4,2] -2.768 2.376 -7.988 -2.486 1.888
beta2_pH[5,2] 0.687 2.892 -6.144 0.904 5.879
beta2_pH[6,2] -1.292 3.312 -7.817 -1.234 5.560
beta2_pH[7,2] -2.168 2.891 -7.881 -2.175 4.142
beta2_pH[8,2] -1.504 2.966 -7.220 -1.496 4.547
beta2_pH[9,2] -1.151 3.093 -7.416 -1.108 4.969
beta2_pH[10,2] -0.727 3.079 -6.815 -0.478 5.325
beta2_pH[11,2] -0.006 3.966 -7.972 1.224 5.986
beta2_pH[12,2] -2.348 1.636 -6.661 -1.864 -0.559
beta2_pH[13,2] -3.682 1.829 -8.180 -3.329 -1.142
beta2_pH[14,2] -3.337 1.750 -7.664 -2.932 -1.065
beta2_pH[15,2] -4.438 1.957 -8.873 -4.236 -1.326
beta2_pH[16,2] -0.121 4.240 -8.369 1.395 6.350
beta2_pH[1,3] 2.353 1.827 0.201 2.006 6.814
beta2_pH[2,3] -1.169 3.730 -7.949 -0.629 5.442
beta2_pH[3,3] -0.282 3.184 -6.411 -0.084 5.920
beta2_pH[4,3] 0.395 2.665 -5.525 0.553 5.876
beta2_pH[5,3] 2.243 2.150 -1.435 1.908 7.048
beta2_pH[6,3] 2.135 2.562 -4.289 2.122 7.010
beta2_pH[7,3] 0.086 2.441 -5.562 0.055 5.302
beta2_pH[8,3] 5.097 2.076 1.759 4.839 9.510
beta2_pH[9,3] 3.101 1.704 0.681 2.783 7.549
beta2_pH[10,3] 1.811 1.650 0.384 1.091 6.472
beta2_pH[11,4] 0.298 3.209 -6.265 0.312 6.543
beta2_pH[12,4] -1.506 1.383 -5.504 -1.062 -0.410
beta2_pH[13,4] 0.158 1.744 -3.692 0.435 3.958
beta2_pH[14,4] 0.163 2.986 -6.614 1.022 4.692
beta2_pH[15,4] 0.455 2.393 -3.983 0.713 5.209
beta2_pH[16,4] 0.106 3.180 -6.866 0.350 5.798
beta2_pH[11,5] -1.726 1.294 -5.440 -1.350 -0.238
beta2_pH[12,5] -2.213 2.012 -6.304 -2.222 3.276
beta2_pH[13,5] -1.184 2.825 -6.088 -1.743 4.846
beta2_pH[14,5] -3.340 1.771 -7.015 -2.946 -0.739
beta2_pH[15,5] -4.510 1.863 -8.456 -4.230 -1.417
beta2_pH[16,5] -0.923 2.874 -5.051 -1.252 4.346
beta3_pH[1,1] 36.146 1.148 34.074 36.087 38.695
beta3_pH[2,1] 33.165 1.795 30.668 32.864 38.480
beta3_pH[3,1] 33.958 1.459 31.438 33.818 37.549
beta3_pH[4,1] 35.622 1.971 32.467 35.420 40.138
beta3_pH[5,1] 27.271 0.474 26.456 27.234 28.141
beta3_pH[6,1] 37.736 3.350 30.682 37.942 43.350
beta3_pH[7,1] 26.941 7.519 19.254 24.711 43.071
beta3_pH[8,1] 38.909 2.189 34.476 38.970 43.189
beta3_pH[9,1] 29.721 1.710 26.790 29.569 33.496
beta3_pH[10,1] 33.556 1.228 31.302 33.545 36.048
beta3_pH[11,1] 31.481 0.996 29.553 31.531 33.255
beta3_pH[12,1] 30.501 0.472 29.584 30.510 31.361
beta3_pH[13,1] 33.244 0.703 32.011 33.183 34.718
beta3_pH[14,1] 32.007 0.511 31.059 32.001 33.025
beta3_pH[15,1] 32.438 0.825 30.845 32.425 34.018
beta3_pH[16,1] 32.505 2.431 29.850 31.786 40.243
beta3_pH[1,2] 31.467 7.594 19.795 29.765 43.357
beta3_pH[2,2] 28.043 5.967 19.481 27.479 41.687
beta3_pH[3,2] 35.418 7.544 19.950 39.579 43.414
beta3_pH[4,2] 26.581 5.837 19.555 25.132 42.038
beta3_pH[5,2] 29.900 6.533 19.684 29.002 42.866
beta3_pH[6,2] 31.656 5.449 20.511 32.879 41.228
beta3_pH[7,2] 27.192 5.813 19.378 26.434 40.724
beta3_pH[8,2] 28.422 6.148 19.564 27.288 41.970
beta3_pH[9,2] 32.147 7.913 19.949 30.503 43.882
beta3_pH[10,2] 30.070 6.681 19.579 28.975 42.469
beta3_pH[11,2] 30.809 8.958 20.202 26.514 43.486
beta3_pH[12,2] 42.056 0.794 40.326 42.118 43.363
beta3_pH[13,2] 43.337 0.373 42.469 43.364 43.922
beta3_pH[14,2] 42.632 0.552 41.327 42.743 43.525
beta3_pH[15,2] 43.251 0.302 42.552 43.260 43.781
beta3_pH[16,2] 31.432 8.814 19.607 28.314 43.615
beta3_pH[1,3] 39.660 1.481 35.264 39.942 41.624
beta3_pH[2,3] 29.356 5.058 20.039 28.968 40.327
beta3_pH[3,3] 31.391 6.141 21.180 30.682 42.506
beta3_pH[4,3] 27.101 5.025 19.594 26.758 40.746
beta3_pH[5,3] 30.359 5.830 19.871 31.016 40.722
beta3_pH[6,3] 30.984 4.971 20.947 31.022 42.232
beta3_pH[7,3] 27.797 6.009 19.490 26.735 42.599
beta3_pH[8,3] 41.498 0.245 41.036 41.498 41.937
beta3_pH[9,3] 33.823 0.623 32.671 33.818 35.005
beta3_pH[10,3] 35.530 0.900 33.433 35.723 36.891
beta3_pH[11,4] 30.563 7.661 19.545 28.538 43.992
beta3_pH[12,4] 41.459 2.834 30.055 42.045 42.764
beta3_pH[13,4] 36.190 5.014 30.025 33.989 43.124
beta3_pH[14,4] 32.899 7.413 20.067 31.115 43.340
beta3_pH[15,4] 29.545 4.913 19.948 30.302 41.201
beta3_pH[16,4] 34.801 5.146 23.252 34.774 42.980
beta3_pH[11,5] 40.125 1.280 36.294 40.197 42.279
beta3_pH[12,5] 37.262 3.603 24.612 37.540 42.492
beta3_pH[13,5] 38.164 3.804 31.596 40.590 41.513
beta3_pH[14,5] 38.959 3.379 25.379 39.630 41.279
beta3_pH[15,5] 40.686 0.425 40.036 40.734 41.334
beta3_pH[16,5] 36.041 4.544 22.802 37.657 40.668
beta0_pelagic[1] 0.967 0.742 -0.364 0.915 2.220
beta0_pelagic[2] 0.974 0.494 -0.038 1.070 1.657
beta0_pelagic[3] 0.217 0.263 -0.435 0.244 0.654
beta0_pelagic[4] 0.257 0.266 -0.266 0.258 0.756
beta0_pelagic[5] 1.293 0.239 0.760 1.329 1.640
beta0_pelagic[6] 1.433 0.223 0.891 1.471 1.777
beta0_pelagic[7] 1.468 0.145 1.149 1.480 1.721
beta0_pelagic[8] 1.681 0.163 1.358 1.684 1.994
beta0_pelagic[9] 1.403 0.370 0.476 1.453 2.017
beta0_pelagic[10] 1.781 0.416 1.097 1.696 2.602
beta0_pelagic[11] 0.257 0.430 -0.806 0.388 0.800
beta0_pelagic[12] 1.626 0.147 1.343 1.623 1.906
beta0_pelagic[13] 0.500 0.148 0.219 0.502 0.777
beta0_pelagic[14] 0.166 0.230 -0.323 0.178 0.575
beta0_pelagic[15] -0.303 0.135 -0.567 -0.306 -0.016
beta0_pelagic[16] 0.286 0.192 -0.156 0.302 0.625
beta1_pelagic[1] 1.806 1.338 0.066 1.431 4.555
beta1_pelagic[2] 0.905 0.852 0.022 0.614 2.990
beta1_pelagic[3] 0.931 0.395 0.418 0.852 1.930
beta1_pelagic[4] 0.967 0.270 0.453 0.961 1.497
beta1_pelagic[5] 0.432 0.408 0.011 0.337 1.404
beta1_pelagic[6] 0.605 0.832 0.019 0.388 3.187
beta1_pelagic[7] 0.657 1.082 0.018 0.338 4.494
beta1_pelagic[8] 0.893 0.638 0.080 0.778 2.404
beta1_pelagic[9] 1.578 0.440 0.849 1.522 2.619
beta1_pelagic[10] 1.200 0.786 0.065 1.058 2.827
beta1_pelagic[11] 2.718 0.794 1.700 2.517 4.658
beta1_pelagic[12] 2.239 0.315 1.653 2.229 2.884
beta1_pelagic[13] 1.938 0.327 1.375 1.909 2.686
beta1_pelagic[14] 2.983 0.568 2.013 2.931 4.254
beta1_pelagic[15] 2.259 0.250 1.790 2.253 2.741
beta1_pelagic[16] 3.230 0.477 2.489 3.163 4.372
beta2_pelagic[1] 1.377 2.128 -2.856 0.901 6.214
beta2_pelagic[2] 0.856 2.153 -4.048 0.131 5.748
beta2_pelagic[3] 1.633 1.721 0.092 0.928 6.113
beta2_pelagic[4] 2.295 1.636 0.267 1.968 6.413
beta2_pelagic[5] -1.372 2.813 -6.669 -1.427 5.087
beta2_pelagic[6] 0.768 2.966 -5.487 0.882 6.333
beta2_pelagic[7] -1.825 2.447 -6.086 -1.943 4.352
beta2_pelagic[8] -2.446 2.051 -7.091 -2.297 0.595
beta2_pelagic[9] 1.774 1.754 0.130 1.151 6.283
beta2_pelagic[10] 1.269 2.142 -2.362 0.416 6.464
beta2_pelagic[11] 0.560 0.562 0.113 0.362 2.039
beta2_pelagic[12] 1.154 0.560 0.468 1.068 2.404
beta2_pelagic[13] 1.125 0.922 0.319 0.825 3.817
beta2_pelagic[14] 0.396 0.229 0.179 0.348 0.892
beta2_pelagic[15] 1.725 0.933 0.700 1.502 4.311
beta2_pelagic[16] 0.680 0.330 0.242 0.623 1.429
beta3_pelagic[1] 25.962 5.084 19.551 23.910 37.534
beta3_pelagic[2] 28.260 4.965 19.683 28.317 37.896
beta3_pelagic[3] 30.071 2.791 24.678 30.107 36.294
beta3_pelagic[4] 25.675 1.702 22.433 25.791 29.393
beta3_pelagic[5] 30.107 4.445 20.841 29.699 38.460
beta3_pelagic[6] 29.591 5.360 20.253 29.594 39.332
beta3_pelagic[7] 28.522 4.427 20.214 29.019 37.270
beta3_pelagic[8] 27.916 3.456 21.335 27.355 36.045
beta3_pelagic[9] 27.437 2.837 23.421 26.576 34.745
beta3_pelagic[10] 26.295 5.160 19.260 25.065 37.567
beta3_pelagic[11] 40.337 1.924 34.796 41.149 41.976
beta3_pelagic[12] 41.791 0.232 41.157 41.865 41.995
beta3_pelagic[13] 41.074 0.761 39.079 41.240 41.968
beta3_pelagic[14] 40.796 1.034 38.212 41.059 41.961
beta3_pelagic[15] 41.807 0.193 41.286 41.867 41.994
beta3_pelagic[16] 41.559 0.452 40.346 41.700 41.989
mu_beta0_pelagic[1] 0.560 0.668 -0.531 0.544 1.683
mu_beta0_pelagic[2] 1.508 0.213 1.056 1.509 1.924
mu_beta0_pelagic[3] 0.415 0.385 -0.333 0.412 1.138
tau_beta0_pelagic[1] 12.197 28.028 0.105 3.091 91.612
tau_beta0_pelagic[2] 42.092 61.083 0.918 13.223 215.009
tau_beta0_pelagic[3] 2.196 1.448 0.327 1.892 5.735
beta0_yellow[1] -0.601 0.193 -1.062 -0.583 -0.265
beta0_yellow[2] 0.458 0.172 0.083 0.467 0.759
beta0_yellow[3] -0.325 0.196 -0.746 -0.310 -0.012
beta0_yellow[4] 0.556 0.423 -0.489 0.676 1.120
beta0_yellow[5] -1.164 0.437 -2.059 -1.151 -0.344
beta0_yellow[6] 0.170 0.224 -0.251 0.166 0.599
beta0_yellow[7] 0.345 0.813 -1.652 0.574 1.281
beta0_yellow[8] 0.712 0.500 -0.726 0.874 1.238
beta0_yellow[9] -0.078 0.274 -0.586 -0.079 0.421
beta0_yellow[10] 0.237 0.153 -0.061 0.237 0.530
beta0_yellow[11] -0.178 0.229 -0.743 -0.160 0.206
beta0_yellow[12] -3.269 0.572 -4.376 -3.278 -2.029
beta0_yellow[13] -3.667 0.461 -4.600 -3.643 -2.781
beta0_yellow[14] -0.534 0.597 -2.517 -0.375 0.059
beta0_yellow[15] -2.152 0.545 -3.072 -2.225 -0.995
beta0_yellow[16] -0.670 0.585 -2.347 -0.477 -0.051
beta1_yellow[1] 0.537 0.609 0.012 0.364 2.141
beta1_yellow[2] 1.225 0.380 0.700 1.168 2.254
beta1_yellow[3] 0.745 0.341 0.304 0.703 1.510
beta1_yellow[4] 2.055 0.951 0.855 1.796 4.446
beta1_yellow[5] 3.222 1.080 1.537 3.092 5.902
beta1_yellow[6] 2.373 0.364 1.693 2.370 3.122
beta1_yellow[7] 1.652 1.525 0.065 1.245 6.007
beta1_yellow[8] 1.843 1.621 0.091 1.365 6.182
beta1_yellow[9] 1.464 0.395 0.767 1.453 2.163
beta1_yellow[10] 2.748 0.517 1.803 2.722 3.822
beta1_yellow[11] 1.420 1.027 0.214 1.099 3.989
beta1_yellow[12] 2.169 0.573 1.040 2.173 3.307
beta1_yellow[13] 2.857 0.466 1.973 2.847 3.814
beta1_yellow[14] 1.470 1.221 0.146 1.078 5.171
beta1_yellow[15] 1.656 0.840 0.426 1.558 4.004
beta1_yellow[16] 0.892 0.792 0.036 0.663 2.901
beta2_yellow[1] -1.020 2.323 -6.140 -0.665 3.885
beta2_yellow[2] -2.201 1.786 -6.442 -1.790 -0.151
beta2_yellow[3] -2.358 1.781 -6.553 -1.988 -0.102
beta2_yellow[4] -0.863 1.301 -4.794 -0.276 -0.062
beta2_yellow[5] -3.018 1.891 -7.479 -2.767 -0.482
beta2_yellow[6] 3.248 1.684 0.944 2.936 7.228
beta2_yellow[7] 0.528 3.083 -5.951 0.659 6.366
beta2_yellow[8] -1.138 2.791 -6.604 -1.155 5.175
beta2_yellow[9] 3.497 1.845 0.479 3.246 7.624
beta2_yellow[10] -3.540 1.844 -7.842 -3.242 -0.855
beta2_yellow[11] -2.411 1.819 -6.193 -2.107 -0.117
beta2_yellow[12] -2.849 1.613 -6.908 -2.589 -0.300
beta2_yellow[13] -2.769 1.393 -6.365 -2.458 -0.931
beta2_yellow[14] -1.648 1.870 -6.345 -1.090 0.511
beta2_yellow[15] -2.341 1.936 -6.947 -1.965 -0.064
beta2_yellow[16] -0.683 2.877 -5.869 -0.848 5.740
beta3_yellow[1] 28.888 4.701 20.281 29.063 37.435
beta3_yellow[2] 29.129 1.654 25.365 28.972 32.670
beta3_yellow[3] 32.508 2.031 27.814 32.584 36.287
beta3_yellow[4] 28.960 3.133 22.870 28.479 35.388
beta3_yellow[5] 33.015 1.259 30.188 33.120 34.962
beta3_yellow[6] 39.514 0.528 38.583 39.496 40.602
beta3_yellow[7] 27.804 3.601 21.115 27.641 36.166
beta3_yellow[8] 28.219 3.491 21.118 28.323 35.272
beta3_yellow[9] 37.329 1.388 35.862 37.451 38.625
beta3_yellow[10] 29.286 0.493 28.098 29.358 29.975
beta3_yellow[11] 31.774 1.917 29.163 31.539 36.408
beta3_yellow[12] 42.800 1.832 36.188 43.186 44.175
beta3_yellow[13] 44.568 0.352 43.775 44.652 44.987
beta3_yellow[14] 32.739 2.996 29.115 32.354 43.077
beta3_yellow[15] 41.879 4.399 30.580 44.214 44.969
beta3_yellow[16] 32.003 3.093 29.068 31.103 42.683
mu_beta0_yellow[1] 0.012 0.433 -0.849 0.016 0.850
mu_beta0_yellow[2] 0.018 0.434 -0.920 0.041 0.855
mu_beta0_yellow[3] -1.484 0.827 -3.051 -1.504 0.267
tau_beta0_yellow[1] 3.226 3.459 0.204 2.213 12.133
tau_beta0_yellow[2] 2.354 3.230 0.218 1.538 9.547
tau_beta0_yellow[3] 0.359 0.285 0.035 0.279 1.083
beta0_black[1] -0.088 0.151 -0.385 -0.092 0.205
beta0_black[2] 1.634 0.406 0.465 1.731 2.052
beta0_black[3] 1.179 0.273 0.579 1.224 1.512
beta0_black[4] 1.829 0.416 0.602 1.924 2.314
beta0_black[5] 1.357 1.105 -0.828 1.349 3.459
beta0_black[6] 1.349 1.258 -1.183 1.348 3.468
beta0_black[7] 1.352 1.167 -0.936 1.344 3.295
beta0_black[8] 1.133 0.289 0.460 1.170 1.588
beta0_black[9] 1.656 0.506 0.673 1.639 2.563
beta0_black[10] 1.358 0.145 1.079 1.360 1.626
beta0_black[11] 3.332 0.247 2.715 3.363 3.689
beta0_black[12] 4.399 0.188 4.042 4.399 4.768
beta0_black[13] -0.081 0.227 -0.529 -0.071 0.334
beta0_black[14] 1.744 0.748 -0.221 1.959 2.625
beta0_black[15] 1.042 0.323 0.195 1.106 1.498
beta0_black[16] 3.359 0.907 0.964 3.678 4.368
beta2_black[1] 3.144 1.661 0.835 2.829 7.192
beta2_black[2] -1.508 2.435 -6.706 -1.273 4.089
beta2_black[3] -0.048 3.170 -6.231 0.096 5.937
beta2_black[4] -2.147 1.956 -6.898 -1.633 -0.057
beta2_black[5] 0.037 3.096 -6.009 0.083 6.136
beta2_black[6] 0.078 3.193 -6.099 0.057 6.341
beta2_black[7] -0.034 3.136 -6.001 -0.043 6.096
beta2_black[8] -3.083 2.147 -7.547 -2.927 0.446
beta2_black[9] -1.401 2.505 -6.579 -1.018 4.184
beta2_black[10] -1.154 3.432 -7.100 -1.301 6.349
beta2_black[11] -1.698 2.316 -6.812 -1.456 3.564
beta2_black[12] -2.729 1.477 -6.483 -2.414 -0.721
beta2_black[13] -2.135 1.531 -6.133 -1.653 -0.422
beta2_black[14] -0.888 1.357 -5.018 -0.325 -0.064
beta2_black[15] -1.728 2.015 -6.466 -1.300 1.714
beta2_black[16] 1.792 2.142 -3.044 1.473 6.414
beta3_black[1] 41.829 0.741 40.216 41.932 43.077
beta3_black[2] 30.060 7.945 19.201 31.064 44.574
beta3_black[3] 27.899 7.249 19.196 27.876 44.495
beta3_black[4] 32.934 3.471 22.592 32.855 39.193
beta3_black[5] 31.831 7.359 19.583 31.665 45.075
beta3_black[6] 31.904 7.400 19.795 31.456 44.975
beta3_black[7] 31.763 7.388 19.720 31.460 44.835
beta3_black[8] 28.551 7.803 20.234 23.306 42.537
beta3_black[9] 34.591 8.304 19.576 35.520 45.219
beta3_black[10] 29.163 9.423 19.453 24.928 45.347
beta3_black[11] 33.863 4.459 29.129 32.303 45.055
beta3_black[12] 32.854 0.591 31.425 32.939 33.782
beta3_black[13] 39.274 0.747 37.656 39.337 40.465
beta3_black[14] 38.050 3.651 30.312 38.417 44.836
beta3_black[15] 36.113 5.028 29.186 35.507 45.269
beta3_black[16] 33.891 4.184 29.145 32.696 43.623
beta4_black[1] -0.269 0.194 -0.648 -0.267 0.100
beta4_black[2] 0.281 0.181 -0.074 0.283 0.626
beta4_black[3] -0.997 0.181 -1.346 -0.996 -0.644
beta4_black[4] 0.640 0.222 0.214 0.640 1.079
beta4_black[5] 0.024 3.187 -6.061 0.078 6.535
beta4_black[6] 0.022 3.265 -6.352 0.020 6.294
beta4_black[7] -0.068 3.144 -6.341 -0.044 6.245
beta4_black[8] -0.848 0.374 -1.599 -0.843 -0.150
beta4_black[9] 2.122 1.114 0.200 2.027 4.613
beta4_black[10] 0.036 0.185 -0.322 0.038 0.392
beta4_black[11] -0.709 0.212 -1.135 -0.710 -0.293
beta4_black[12] 0.563 0.341 -0.096 0.564 1.259
beta4_black[13] -1.280 0.218 -1.709 -1.281 -0.855
beta4_black[14] -0.046 0.236 -0.504 -0.053 0.412
beta4_black[15] -0.940 0.219 -1.360 -0.942 -0.515
beta4_black[16] -0.583 0.233 -1.044 -0.588 -0.108
mu_beta0_black[1] 1.016 0.867 -0.823 1.102 2.393
mu_beta0_black[2] 1.308 0.671 -0.009 1.350 2.316
mu_beta0_black[3] 1.980 1.163 -0.707 2.121 3.767
tau_beta0_black[1] 1.241 1.164 0.047 0.930 4.405
tau_beta0_black[2] 21.289 40.114 0.091 6.416 126.446
tau_beta0_black[3] 0.319 0.222 0.029 0.272 0.886
beta0_dsr[11] -3.069 0.256 -3.590 -3.059 -2.596
beta0_dsr[12] 4.569 0.304 3.987 4.569 5.142
beta0_dsr[13] -1.840 0.716 -3.731 -1.616 -0.893
beta0_dsr[14] -4.267 0.397 -4.937 -4.288 -3.447
beta0_dsr[15] -2.454 0.290 -3.009 -2.453 -1.832
beta0_dsr[16] -3.121 0.346 -3.794 -3.121 -2.434
beta1_dsr[11] 4.921 0.269 4.415 4.911 5.465
beta1_dsr[12] 4.324 1.729 1.525 4.126 8.338
beta1_dsr[13] 3.799 1.146 2.519 3.317 6.573
beta1_dsr[14] 6.921 0.431 6.063 6.937 7.693
beta1_dsr[15] 3.587 0.298 2.973 3.587 4.142
beta1_dsr[16] 5.905 0.365 5.191 5.899 6.623
beta2_dsr[11] -6.282 1.498 -9.323 -6.190 -3.643
beta2_dsr[12] -3.328 1.719 -7.069 -3.121 -0.716
beta2_dsr[13] -1.710 1.685 -5.924 -1.118 -0.159
beta2_dsr[14] -3.708 1.352 -7.197 -3.425 -1.864
beta2_dsr[15] -5.145 1.640 -8.721 -4.993 -2.398
beta2_dsr[16] -5.773 1.558 -9.131 -5.610 -3.160
beta3_dsr[11] 43.478 0.129 43.236 43.476 43.726
beta3_dsr[12] 33.504 0.953 31.053 33.722 34.738
beta3_dsr[13] 42.654 1.234 39.184 43.015 44.226
beta3_dsr[14] 43.379 0.147 43.135 43.365 43.707
beta3_dsr[15] 43.438 0.172 43.130 43.433 43.779
beta3_dsr[16] 43.452 0.136 43.200 43.446 43.726
beta4_dsr[11] 0.732 0.220 0.309 0.732 1.157
beta4_dsr[12] 0.197 0.702 -1.066 0.164 1.649
beta4_dsr[13] -0.173 0.215 -0.593 -0.171 0.256
beta4_dsr[14] 0.197 0.273 -0.319 0.191 0.739
beta4_dsr[15] 1.136 0.209 0.725 1.131 1.551
beta4_dsr[16] 0.173 0.241 -0.295 0.170 0.643
beta0_slope[11] -2.004 0.165 -2.325 -2.007 -1.682
beta0_slope[12] -4.604 0.228 -4.967 -4.618 -4.128
beta0_slope[13] -1.575 0.284 -2.247 -1.531 -1.165
beta0_slope[14] -2.760 0.184 -3.128 -2.764 -2.399
beta0_slope[15] -2.351 1.111 -4.823 -1.801 -1.443
beta0_slope[16] -2.820 0.173 -3.150 -2.826 -2.475
beta1_slope[11] 4.408 0.301 3.837 4.408 4.998
beta1_slope[12] 5.022 0.573 3.888 5.025 6.127
beta1_slope[13] 2.741 0.508 1.988 2.662 4.128
beta1_slope[14] 5.890 0.702 4.638 5.833 7.356
beta1_slope[15] 2.918 1.614 1.555 2.156 6.589
beta1_slope[16] 5.317 0.385 4.573 5.313 6.053
beta2_slope[11] 5.856 1.440 3.449 5.797 8.928
beta2_slope[12] 3.756 1.809 1.119 3.454 7.901
beta2_slope[13] 2.118 1.587 0.275 1.792 6.051
beta2_slope[14] 1.340 0.474 0.774 1.256 2.353
beta2_slope[15] 3.162 2.356 0.051 3.327 7.858
beta2_slope[16] 5.340 1.608 2.529 5.222 8.877
beta3_slope[11] 43.482 0.135 43.235 43.480 43.749
beta3_slope[12] 43.361 0.277 42.824 43.345 43.953
beta3_slope[13] 43.112 0.881 40.676 43.288 44.197
beta3_slope[14] 44.251 0.355 43.527 44.249 44.901
beta3_slope[15] 41.792 3.445 32.293 43.477 44.088
beta3_slope[16] 43.470 0.152 43.199 43.463 43.777
beta4_slope[11] -0.476 0.227 -0.922 -0.478 -0.027
beta4_slope[12] -2.394 0.759 -3.963 -2.381 -1.016
beta4_slope[13] 0.289 0.224 -0.150 0.287 0.725
beta4_slope[14] -0.026 0.272 -0.555 -0.025 0.513
beta4_slope[15] -0.170 0.209 -0.563 -0.177 0.244
beta4_slope[16] -0.069 0.242 -0.549 -0.069 0.401
sigma_H[1] 0.215 0.055 0.118 0.210 0.334
sigma_H[2] 0.175 0.030 0.124 0.173 0.241
sigma_H[3] 0.190 0.042 0.115 0.189 0.278
sigma_H[4] 0.421 0.077 0.299 0.412 0.599
sigma_H[5] 0.975 0.209 0.596 0.959 1.398
sigma_H[6] 0.395 0.195 0.043 0.388 0.811
sigma_H[7] 0.305 0.062 0.209 0.296 0.448
sigma_H[8] 0.415 0.088 0.265 0.408 0.608
sigma_H[9] 0.522 0.122 0.332 0.507 0.783
sigma_H[10] 0.210 0.041 0.138 0.206 0.302
sigma_H[11] 0.275 0.045 0.199 0.271 0.372
sigma_H[12] 0.446 0.162 0.213 0.428 0.764
sigma_H[13] 0.215 0.038 0.151 0.211 0.299
sigma_H[14] 0.508 0.093 0.346 0.501 0.707
sigma_H[15] 0.250 0.043 0.178 0.246 0.346
sigma_H[16] 0.219 0.043 0.148 0.215 0.316
lambda_H[1] 2.514 3.209 0.117 1.422 11.251
lambda_H[2] 8.017 7.673 0.714 5.776 28.904
lambda_H[3] 6.627 9.680 0.294 3.349 32.806
lambda_H[4] 0.006 0.004 0.001 0.006 0.018
lambda_H[5] 3.208 8.425 0.025 0.661 26.254
lambda_H[6] 6.902 13.815 0.008 0.516 47.113
lambda_H[7] 0.014 0.010 0.002 0.011 0.040
lambda_H[8] 8.019 10.031 0.124 4.617 36.156
lambda_H[9] 0.015 0.011 0.003 0.013 0.043
lambda_H[10] 0.273 0.510 0.031 0.181 0.921
lambda_H[11] 0.246 0.357 0.011 0.129 1.144
lambda_H[12] 5.028 7.746 0.201 2.774 24.647
lambda_H[13] 3.274 2.980 0.195 2.456 11.104
lambda_H[14] 3.627 4.637 0.215 2.184 16.127
lambda_H[15] 0.039 0.149 0.003 0.019 0.182
lambda_H[16] 0.731 1.105 0.040 0.369 3.460
mu_lambda_H[1] 4.332 1.875 1.182 4.178 8.320
mu_lambda_H[2] 3.688 1.926 0.557 3.544 7.766
mu_lambda_H[3] 3.488 1.840 0.746 3.238 7.667
sigma_lambda_H[1] 8.644 4.267 1.976 8.043 18.237
sigma_lambda_H[2] 8.095 4.621 0.924 7.490 18.001
sigma_lambda_H[3] 6.194 3.937 0.933 5.412 15.876
beta_H[1,1] 6.822 1.211 3.901 6.993 8.646
beta_H[2,1] 9.871 0.494 8.872 9.891 10.788
beta_H[3,1] 7.972 0.745 6.173 8.066 9.209
beta_H[4,1] 9.422 7.836 -6.662 9.558 23.976
beta_H[5,1] 0.029 2.598 -5.519 0.247 4.378
beta_H[6,1] 2.865 4.247 -7.566 4.361 7.853
beta_H[7,1] 0.914 5.707 -11.136 1.502 10.968
beta_H[8,1] 1.279 3.369 -2.268 1.242 3.411
beta_H[9,1] 13.349 5.700 2.136 13.241 24.774
beta_H[10,1] 7.123 1.731 3.668 7.193 10.469
beta_H[11,1] 5.223 3.420 -2.659 5.849 9.933
beta_H[12,1] 2.640 1.016 0.855 2.563 4.887
beta_H[13,1] 9.040 0.944 6.837 9.119 10.521
beta_H[14,1] 2.215 1.027 0.220 2.246 4.282
beta_H[15,1] -5.150 4.488 -12.735 -5.473 4.517
beta_H[16,1] 3.524 2.662 -0.735 3.169 9.999
beta_H[1,2] 7.906 0.263 7.367 7.915 8.389
beta_H[2,2] 10.028 0.138 9.767 10.024 10.305
beta_H[3,2] 8.940 0.195 8.552 8.941 9.326
beta_H[4,2] 3.536 1.480 0.881 3.465 6.682
beta_H[5,2] 1.954 0.976 -0.046 1.971 3.790
beta_H[6,2] 5.681 1.101 3.284 5.877 7.427
beta_H[7,2] 2.513 1.139 0.459 2.423 4.961
beta_H[8,2] 2.991 1.002 1.382 3.119 4.193
beta_H[9,2] 3.426 1.101 1.246 3.413 5.700
beta_H[10,2] 8.185 0.359 7.443 8.190 8.872
beta_H[11,2] 9.725 0.612 8.814 9.601 11.107
beta_H[12,2] 3.943 0.361 3.273 3.928 4.684
beta_H[13,2] 9.111 0.263 8.638 9.095 9.661
beta_H[14,2] 4.023 0.345 3.362 4.023 4.707
beta_H[15,2] 11.131 0.826 9.416 11.195 12.598
beta_H[16,2] 4.460 0.827 2.991 4.428 6.234
beta_H[1,3] 8.492 0.262 8.001 8.480 9.019
beta_H[2,3] 10.080 0.117 9.847 10.078 10.320
beta_H[3,3] 9.631 0.164 9.324 9.626 9.973
beta_H[4,3] -2.493 0.869 -4.220 -2.466 -0.807
beta_H[5,3] 3.983 0.630 2.696 3.999 5.226
beta_H[6,3] 8.186 1.247 6.402 7.867 10.774
beta_H[7,3] -2.572 0.794 -4.117 -2.572 -1.048
beta_H[8,3] 5.209 0.475 4.625 5.155 6.054
beta_H[9,3] -2.779 0.748 -4.278 -2.772 -1.360
beta_H[10,3] 8.757 0.280 8.232 8.751 9.323
beta_H[11,3] 8.548 0.274 7.952 8.568 9.025
beta_H[12,3] 5.247 0.302 4.543 5.283 5.760
beta_H[13,3] 8.812 0.181 8.441 8.817 9.144
beta_H[14,3] 5.685 0.273 5.109 5.706 6.168
beta_H[15,3] 10.363 0.345 9.704 10.360 11.049
beta_H[16,3] 6.072 0.586 4.830 6.114 7.104
beta_H[1,4] 8.215 0.198 7.792 8.231 8.564
beta_H[2,4] 10.133 0.119 9.878 10.141 10.352
beta_H[3,4] 10.108 0.165 9.738 10.121 10.396
beta_H[4,4] 11.766 0.438 10.904 11.765 12.623
beta_H[5,4] 5.744 0.827 4.405 5.647 7.651
beta_H[6,4] 7.062 0.952 4.937 7.314 8.413
beta_H[7,4] 8.250 0.357 7.561 8.253 8.954
beta_H[8,4] 6.687 0.246 6.223 6.694 7.117
beta_H[9,4] 7.208 0.471 6.286 7.208 8.130
beta_H[10,4] 7.735 0.239 7.285 7.730 8.247
beta_H[11,4] 9.285 0.203 8.872 9.284 9.687
beta_H[12,4] 7.127 0.208 6.723 7.125 7.563
beta_H[13,4] 9.002 0.147 8.706 9.001 9.290
beta_H[14,4] 7.677 0.209 7.273 7.679 8.088
beta_H[15,4] 9.351 0.284 8.769 9.361 9.875
beta_H[16,4] 9.316 0.238 8.890 9.306 9.800
beta_H[1,5] 8.989 0.154 8.679 8.991 9.281
beta_H[2,5] 10.789 0.095 10.609 10.787 10.986
beta_H[3,5] 10.902 0.170 10.602 10.889 11.258
beta_H[4,5] 8.403 0.461 7.506 8.397 9.326
beta_H[5,5] 5.292 0.656 3.759 5.379 6.388
beta_H[6,5] 8.828 0.628 7.889 8.713 10.281
beta_H[7,5] 6.795 0.344 6.137 6.788 7.481
beta_H[8,5] 8.212 0.207 7.862 8.198 8.629
beta_H[9,5] 8.200 0.470 7.263 8.210 9.122
beta_H[10,5] 10.124 0.227 9.672 10.125 10.570
beta_H[11,5] 11.550 0.232 11.087 11.554 12.017
beta_H[12,5] 8.479 0.199 8.087 8.476 8.883
beta_H[13,5] 10.010 0.133 9.755 10.008 10.275
beta_H[14,5] 9.207 0.231 8.793 9.194 9.682
beta_H[15,5] 11.049 0.295 10.473 11.056 11.602
beta_H[16,5] 9.943 0.173 9.602 9.943 10.280
beta_H[1,6] 10.251 0.211 9.898 10.230 10.726
beta_H[2,6] 11.517 0.108 11.302 11.518 11.726
beta_H[3,6] 10.815 0.159 10.472 10.827 11.093
beta_H[4,6] 12.862 0.823 11.217 12.875 14.498
beta_H[5,6] 5.857 0.645 4.691 5.837 7.223
beta_H[6,6] 8.736 0.682 6.968 8.851 9.748
beta_H[7,6] 9.847 0.566 8.732 9.852 10.949
beta_H[8,6] 9.526 0.264 9.007 9.544 9.971
beta_H[9,6] 8.478 0.790 6.924 8.476 10.106
beta_H[10,6] 9.521 0.324 8.811 9.553 10.090
beta_H[11,6] 10.796 0.359 10.002 10.821 11.440
beta_H[12,6] 9.384 0.256 8.899 9.380 9.913
beta_H[13,6] 11.063 0.164 10.757 11.056 11.429
beta_H[14,6] 9.890 0.288 9.292 9.901 10.430
beta_H[15,6] 11.009 0.469 10.071 11.005 11.938
beta_H[16,6] 10.539 0.246 10.005 10.555 10.987
beta_H[1,7] 10.830 1.006 8.268 11.002 12.353
beta_H[2,7] 12.225 0.446 11.335 12.217 13.151
beta_H[3,7] 10.598 0.641 9.204 10.648 11.703
beta_H[4,7] 2.520 4.215 -5.733 2.426 10.936
beta_H[5,7] 6.474 2.072 2.797 6.328 11.272
beta_H[6,7] 9.435 2.504 4.363 9.461 15.413
beta_H[7,7] 10.621 2.785 5.251 10.643 16.103
beta_H[8,7] 10.947 0.912 9.447 10.919 12.553
beta_H[9,7] 4.373 4.055 -3.798 4.515 12.072
beta_H[10,7] 9.916 1.482 7.255 9.819 13.166
beta_H[11,7] 11.041 1.740 7.852 10.919 14.899
beta_H[12,7] 10.020 0.943 7.932 10.095 11.621
beta_H[13,7] 11.690 0.756 9.833 11.771 12.907
beta_H[14,7] 10.523 0.934 8.454 10.570 12.272
beta_H[15,7] 11.280 2.475 6.351 11.283 16.105
beta_H[16,7] 12.501 1.318 10.407 12.303 15.532
beta0_H[1] 8.633 15.289 -21.794 8.668 37.737
beta0_H[2] 10.562 6.583 -2.703 10.562 23.758
beta0_H[3] 9.625 9.885 -9.851 9.766 27.999
beta0_H[4] 5.241 180.406 -367.001 6.190 367.447
beta0_H[5] 4.658 28.417 -52.899 4.515 67.654
beta0_H[6] 6.732 50.854 -110.335 7.724 122.336
beta0_H[7] 5.418 129.469 -252.170 4.491 263.532
beta0_H[8] 6.525 31.931 -16.377 6.295 28.443
beta0_H[9] 7.337 120.394 -225.720 8.357 251.789
beta0_H[10] 9.511 33.116 -53.926 8.638 79.625
beta0_H[11] 8.631 49.593 -98.345 9.364 108.999
beta0_H[12] 6.798 11.942 -15.082 6.630 28.996
beta0_H[13] 9.447 11.957 -11.384 9.768 30.762
beta0_H[14] 6.808 10.961 -15.640 6.781 27.498
beta0_H[15] 7.584 102.039 -203.849 8.254 202.351
beta0_H[16] 8.526 26.330 -42.245 8.443 62.534